Several Algorithms Of Bi-level Multi-objective Problem

There are optimization problems in the areas of human life,production and practice,in which the decision-making optimization problems is one of the most attractive problem.Withing the development of various fields rapidly,the bi-level programming problem with hierarchical structure has emerged at the right moment.However,the bi-level programming problem has been proved to be NP-hard problem.In this dissertation,under convexity assumptions(assuming that the objective functions are strictly convexity function and the constraint sets are convex sets)conditions,several algorithms of nonlinear bi-level multi-objective programming problem is studied with the purpose of provide more non-inferior solutions to the decision maker and let he or she has more choices. The main contributions of this dissertation are as follows:First,the basic knowledge are introduced when research bi-level multi-objective programming problem necessarily,including the some basic concept of the convex sets,convex functions, some basic theorem of extreme value, the models and basic algorithms of linear programming and non-linear programming,in order to the foundation for the later study.Second,some knowledge about the single-level multi-objective programming problem are introduced,including its basic model,basic algorithms and give some examples to illustrate the algorithm is effective.Because one of the important approach which study the bi-level multi-objective programming problem is turn bi-level programming to single-level programming,so it is basic to master the algorithms of the single-level multi-objective programming problem.Thirdly,according to the upper variable in the role of the lower decision,bi-level multi-objective programming can be divided into two categories.On one hand,it is discussed that upper variable be the parameter,according to the thought that bi-level programming is transformed into equivalent single-level programming,turn the non-linear bi-level multi-objective programming into equivalent non-linear single-level multi-objective programming using the linear weighted method,ideal point method that based on square weighted,an improved penalty function method,and weighted geometric method.On the other hand,it is discussed that upper variable be the constraint,regard the lower problem as independent decision-making problem.After it making a decision independently,bring the solutions which satisfied the constraint conditions into the upper problem and solution it.Examples are given for the algorithms to illustrate it is effective.Fourthly,two kinds of special non-linear bi-level multi-objective programming problem are discussed.When the constraint conditions is linear,using the Lagrange multiplier method to solve it.When the lower problem is linear multi-objective programming and the upper problem is non-linear multi-objective programming,solve the optimal solution of the lowerproblem and let it into the upper problem can get the efficient solution.